• Exploratory Data Analysis (EDA)
  
• Powerful environment for visualizing scientific data
• Fully programmable
• An example of Exploratory Data Analysis will be performed with the Iris data set.

• plot: generic x-y plotting
• barplot: bar plots
• boxplot: box-and-whisker plot
• hist: histograms
• pie: pie charts
• dotchart: cleveland dot plots
• image, heatmap, contour, persp: functions to generate image-like plots
• qqnorm, qqline, qqplot: distribution comparison plots
• pairs, coplot, matplot: display of multivariant data Help on these functions

The iris data set is available at the UCI Machine Learning Repository.

The data set was created by statistician Douglas Fisher. The data consists of 3 classes of flower types:

• setosa
• virginica
• versicolor

The data has 4 attributes:

• sepal width
• sepal length
• petal width
• petal length

The data needs to be loaded into R.

head(iris)

##   Sepal.Length Sepal.Width Petal.Length Petal.Width Species
## 1          5.1         3.5          1.4         0.2  setosa
## 2          4.9         3.0          1.4         0.2  setosa
## 3          4.7         3.2          1.3         0.2  setosa
## 4          4.6         3.1          1.5         0.2  setosa
## 5          5.0         3.6          1.4         0.2  setosa
## 6          5.4         3.9          1.7         0.4  setosa

names(iris)

## [1] "Sepal.Length" "Sepal.Width"  "Petal.Length" "Petal.Width" 
## [5] "Species"

The summary function can be used to assess the statistical properties of each attribute.

summary(iris[,-5])

##   Sepal.Length    Sepal.Width     Petal.Length    Petal.Width   
##  Min.   :4.300   Min.   :2.000   Min.   :1.000   Min.   :0.100  
##  1st Qu.:5.100   1st Qu.:2.800   1st Qu.:1.600   1st Qu.:0.300  
##  Median :5.800   Median :3.000   Median :4.350   Median :1.300  
##  Mean   :5.843   Mean   :3.057   Mean   :3.758   Mean   :1.199  
##  3rd Qu.:6.400   3rd Qu.:3.300   3rd Qu.:5.100   3rd Qu.:1.800  
##  Max.   :7.900   Max.   :4.400   Max.   :6.900   Max.   :2.500

other statistics may be calculated as described in the introduction to R examples.

• plot x versus y

plot(iris[,1], iris[,2],xlab=names(iris)[1],ylab=names(iris)[2],col=2)

set.seed(100)
y <- matrix(runif(30), ncol=3, dimnames=list(letters[1:10], LETTERS[1:3]))
plot(y[,1], y[,2], pch=20, col="red", main="Symbols and Labels")
text(y[,1]+0.03, y[,2], rownames(y))

plot(y[,1], y[,2])
myline <- lm(y[,2]~y[,1]);
abline(myline, lwd=2)

plot(y[,1], y[,2])
text(y[1,1], y[1,2]+.2,expression(sum(frac(1,sqrt(x^2*pi)))), cex=1.3)

• Set the number of breaks to 9, therefore, there will be 10 equal sized bins.

par(mfrow=c(1,2))
hist(iris$Petal.Width, breaks=9)
hist(iris$Petal.Width, breaks=19)

Note, the number of breaks can be a single number, vector, function to evaluate points or character string.

b <- seq(min(iris$Petal.Width), max(iris$Petal.Width),
            length=11)
hist(iris$Petal.Width, breaks=b, col="blue", xlab="Petal Width",
     main="Histogram of Petal Width")

Density plots can be viewed as smoothed versions of a histogram. We can estimate the density using R's density function

dens.pw = density(iris$Petal.Width)
plot(dens.pw, ylab = "f(width)", xlab = "width", main= "Density of Petal Width")

Let's also look at the density function of petal.length for each of the three classes of irises.

density.setosa = density(iris$Petal.Length[iris$Species == "setosa"])
density.versicolor = density(iris$Petal.Length[iris$Species == "versicolor"])
density.virginica = density(iris$Petal.Length[iris$Species == "virginica"])

plot(density.setosa, ylab="f(length)", xlab="length (cm)", main="Density plot of Petal
     Legnths", xlim = c(0,8), lwd=4, col="red")
lines(density.versicolor, col="blue", lwd=4)
lines(density.virginica, col="green", lwd=4)
legend(4, 2.5, c("Setosa", "Versicolor", "Virginica"), lwd=rep(4,3),
       col=c("red", "blue", "green"))

The cumulative area under the density function is the cumulative distribution function. Looking at this function using a sample of points gives use the empirical cumulative distribution function (ECDF). Let's start by calculating the cumulative areas

ecdf.setosa = ecdf(iris$Petal.Length[iris$Species == "setosa"])
ecdf.versicolor = ecdf(iris$Petal.Length[iris$Species == "versicolor"])
ecdf.virginica = ecdf(iris$Petal.Length[iris$Species == "virginica"])

The functions may also be plotted (notice the step function patterns)

plot(ecdf.setosa, ylab = "F(length)", xlab = "length (cm)", col.h = "red",
     main = "ECDF for Petal Lengths",
      verticals = T, col.v = "red", do.p = F, lwd = 4, xlim = c(0, 8))
lines(ecdf.versicolor, col.h = "blue", col.v = "blue", verticals = T, lwd = 4,
        do.p = F)
lines(ecdf.virginica, col.h = "green", col.v = "green", verticals = T, lwd = 4,
        do.p = F)

The inverse of the ECDF is the quantile function.

ps = seq(0,1,length=25)
quantile.setosa = quantile(iris$Petal.Length[iris$Species == "setosa"], probs=ps)
quantile.setosa

##        0% 4.166667% 8.333333%     12.5% 16.66667% 20.83333%       25% 
##  1.000000  1.200000  1.300000  1.300000  1.300000  1.320833  1.400000 
## 29.16667% 33.33333%     37.5% 41.66667% 45.83333%       50% 54.16667% 
##  1.400000  1.400000  1.400000  1.400000  1.400000  1.500000  1.500000 
## 58.33333%     62.5% 66.66667% 70.83333%       75% 79.16667% 83.33333% 
##  1.500000  1.500000  1.500000  1.500000  1.575000  1.600000  1.600000 
##     87.5% 91.66667% 95.83333%      100% 
##  1.600000  1.700000  1.700000  1.900000

quantile.versicolor = quantile(iris$Petal.Length
                               [iris$Species == "versicolor"],probs=ps)
quantile.virginica = quantile(iris$Petal.Length
                              [iris$Species == "virginica"], probs=ps)
plot(ps, quantile.setosa, xlab = "p", ylab = "length (cm)",
     main = "Quantiles for Petal Length",
     type="l", lwd = 4, col="red", ylim=c(0,8))
lines(ps, quantile.versicolor, col = "blue", lwd = 4)
lines(ps, quantile.virginica, col = "green", lwd = 4)

hist(iris$Sepal.Length, probability=TRUE, breaks=15, col="light blue")
rug(jitter(iris$Sepal.Length, 5))
points(density(iris$Sepal.Length), type='l', lwd=3, col='red')
f <- function(t) {
  dnorm(t, mean=mean(iris$Sepal.Length), sd=sd(iris$Sepal.Length) )
}
curve(f, add=T, col="blue", lwd=3, lty=2)

A q-q plot is a plot of the quantiles of the first data set against the quantiles of the second data set.

x <- iris$Sepal.Length
qqnorm(x)
qqline(x, col="red", lwd=3)

par(mfrow=c(1,2))
x <- rnorm(100)
y <- rnorm(100)^2
qqnorm(x, main="Gaussian variable");qqline(x, col="blue", lwd=3)
qqnorm(y, main="Non gaussian variable");qqline(y, col="red", lwd=3)

Box plots are used to compactly show many pieces of information about a variables distribution including some summary statistics.

A box plot of each attribute of the iris data set

boxplot(iris[,-1])

A box plot may also be used for one attribute petal.length and show how it varies with the class Species

boxplot(iris$Petal.Length ~ iris$Species)

Scatter plots are used to plot two variables against each other (or 3 in the case of 3D plots).

plot(iris$Petal.Length, iris$Sepal.Width)

For data sets with only a few attributes, all the pairwise scatter plots may be constructed.

pairs(as.matrix(iris[,-5]), pch=21, bg=c("red", "blue", "green")[(iris$Species)])

Default color palette and how to change it

palette()

## [1] "black"   "red"     "green3"  "blue"    "cyan"    "magenta" "yellow" 
## [8] "gray"

palette(rainbow(5, start=0.1, end=0.2))
palette()

## [1] "#FF9900" "#FFBF00" "#FFE600" "#F2FF00" "#CCFF00"

The gray function allows to select any type of gray shades by providing values from 0 to 1

pie(1:5,col=gray(seq(0.1, 1, by= 0.2)))

library(gplots,warn.conflicts = F)

## Warning: package 'gplots' was built under R version 3.5.2

par(mfrow=c(1,2))
pie(1:50, col=colorpanel(50,"red","black","green"))
pie(1:50, col=rainbow(50))

The layout function allows to divide the plotting device into variable numbers of rows and columns with the column-widths and the row-heights specified in the respective arguments.

nf <- layout(matrix(c(2,1,3,3), 2, 2, byrow=TRUE), c(3,7), c(5,3))
layout.show(nf)

x <- rnorm(100) ; y <- rnorm(100)
layout(matrix(c(2,1,3,3), 2, 2, byrow=TRUE), c(3,7), c(5,4))
plot(x,y)
boxplot(y,horizontal = FALSE,col=2)
hist(x,col=4)

data(cars)
layout( matrix( c(2,1,0,3), 2, 2, byrow=T ),
c(1,6), c(4,1))
par(mar=c(1,1,5,2)); plot(cars$dist ~ cars$speed,xlab='', ylab='',las = 1)
rug(side=1, jitter(cars$speed, 5) );rug(side=2, jitter(cars$dist, 20) );
title(main = "cars data")
par(mar=c(1,2,5,1))
boxplot(cars$dist, axes=F); title(ylab='Stopping distance (ft)', line=0)
par(mar=c(5,1,1,2))
boxplot(cars$speed, horizontal=T, axes=F); title(xlab='Speed (mph)', line=1)

• Consider the same approach in this slides for barplot

After the pdf() command all graphs are redirected to file test.pdf. Works for all common formats similarly: jpeg, png, ps, tiff, …

pdf("test.pdf"); plot(1:10, 1:10); dev.off()

x <- seq(-10, 10, length= 30)
y <- x
f <- function(x, y) { r <- sqrt(x^2+y^2); 10 * sin(r)/r }
z <- outer(x, y, f)
persp(x, y, z, theta = 30, phi = 30, expand = 0.5, col = "lightblue")

A contour plot is a graphical technique for representing a 3-dimensional surface by plotting constant z slices, called contours, on a 2-dimensional format.

contour(x,y,z) # or contour(z)

Density estimation is available for higher dimensional data. Use the MASS package.

library(MASS)
petal.dens = kde2d(iris$Petal.Length, iris$Petal.Width)
contour(petal.dens)

The plot may aslo be viewed as an image

image(petal.dens)

• High-level graphics system
• Implements Trellis graphics system from S-Plus Simplifies high-level plotting tasks: arranging complex graphical features
• Syntax similar to R’s base graphics

library(lattice)
xyplot(1:8 ~ 1:8 | rep(LETTERS[1:4], each=2), as.table=TRUE)

parallelplot(~iris[1:4] | Species, iris, horizontal.axis = FALSE,
             layout = c(1, 3, 1))

• What is ggplot2?
  • High-level graphics system
  • Streamlines many graphics workflows for complex plots
  • Simpler qplot function provides many shortcuts
• ggplot function accepts two arguments
  • Data set to be plotted
  • Aesthetic mappings provided by aes function
  • Additional parameters such as geometric objects (e.g. points, lines, bars) are passed on by appending them with + as separator.

qplot syntax is similar to R’s basic plot function Arguments:

• x: x-coordinates (e.g. col1)
• y: y-coordinates (e.g. col2)
• data: data frame with corresponding column names xlim, ylim: e.g. xlim=c(0,10)
• log: e.g. log="x" or log="xy"
• main: main title; see ?plotmath for mathematical formula xlab, ylab: labels for the x- and y-axes
• color, shape, size
• …: many arguments accepted by plot function

Create sample data

library(ggplot2,quietly = T)
#cat <- rep(c("A", "B"), 5)
qplot(iris$Sepal.Length, iris$Sepal.Width, geom="point")

qplot(Sepal.Length, Petal.Width, data = iris, geom="point",
      size=Petal.Length,col=Species,
      main="Dot Size and Color Relative to Some Values")

qplot(Sepal.Length, Petal.Width, data = iris, geom="point",col=Species)+
       theme(legend.position = "none")

qplot(Sepal.Length, Petal.Width, data = iris, geom="point",
      shape=iris$Species,size=2)

qplot(Sepal.Length, Petal.Width, data = iris, geom = c("point"))+
            geom_smooth(method=lm,col=2)

qplot(Sepal.Length, Petal.Width, data = iris, facets = Species ~ Petal.Length)